A manufactured product has a constant monthly demand of 1,200 units. The machine used to manufacture this product has a constant yearly production rate of 18,000 units and a setup cost of $120. The unit variable production cost is $100 and the annual inventory carrying cost is 0.1.
1- Find the minimum yearly total system cost when shortages are not allowed.
The production manager would like now to allow for shortages provided that the maximum stockouts will remain equal to one sixth (1/6) of the minimum batch size. Find the unit yearly shortage cost. What is the minimum inventory cost in this case?